Abstract
This paper proposes a model algorithm control (MAC) method for the path tracking control of differentially steered wheeled mobile robots (WMRs) subject to nonholonomic constraints. The continuous dynamic model of the wheeled mobile robot is presented and used as the model to be controlled. The MAC controller is designed based on the sampled-data representation of the system. In this paper the case that there exists time delay in the control input is also considered. A time discretization method using the Taylor series and the zero-order-hold (ZOH) assumption is proposed to discretize the continuous dynamic model of the WMR. This time discretization method is especially useful in the case of the time delayed system. It can provide finite dimensional and more accurate discretized form model of the mobile robot with input time delay and convert it into a general nonlinear time discretized form to which the MAC controller can be applied. Simulations are conducted to show the performance and feasibility of the proposed control strategy. In these simulations the WMR is controlled to track two difference reference paths such as the “8” shape path and the circular path. The bounded inertial parameters uncertainties and some disturbance are also considered in the model of the control system.
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Kolmanovsky, I. and McClamroch, N. H., “Developments in nonholonomic control problems,” IEEE Control Syst. Mag., Vol. 15, No. 6, pp. 20–36, 1995.
Bloch, A. M., McClamroch, N. H. and Reyhanoglu, M., “Controllability and stabilizability of properties of a nonholonomic control systems,” Proceedings of the 29th Conference on Decision and Control, pp. 1312–1314, 1990.
Divelbiss, A. W. and Wen, J. T., “Trajectory tracking control of a car-trailer system,” IEEE Transactions on Control Systems Technology, Vol. 5, No. 3, pp. 269–278, 1997.
Koo, T. Y., Park, K. J., Kim, B. Y., Kim, H. J. and Suh, M. W., “A Study on Driver’s Workload of Telematics Using a Driving Simulator: A Comparison among Information Modalities,” Int. J. Precis. Eng. Manuf., Vol. 10, No. 3, pp. 59–63, 2009.
Choi, K. S. and Lee, S. G., “Enhanced SLAM for a Mobile Robot using Extended Kalman Filter and Neural Networks,” Int. J. Precis. Eng. Manuf., Vol. 11, No. 2, pp. 255–264, 2010.
Kanayama, Y., Kimura, Y., Miyazaki, F. and Noguchi, T., “A Stable Tracking Control Method For A Non-holonomic Mobile Robot,” Proc. of IEEE/RSJ International Workshop on Intelligent Robots and Systems, Vol. 3, pp. 1236–1241, 1991.
Mutambara, A. G. O. and Durrant-Whyte, H. E., “Estimation and Control for A Modular Wheeled Mobile Robot,” IEEE Transactions on Control Systems Technology, Vol. 8, No. 1, pp. 35–46, 2000.
Letizia Corradini, M., Leo, T. and Orlando, G., “Experimental Testing Of A Discrete-Time Sliding Mode Controller For Trajectory Tracking Of A Wheeled Mobile Robot In The Presence Of Skidding Effects,” Journal of Robotic Systems, Vol. 19, No. 4, pp. 177–188, 2002.
De Wit, C. C. and Sordalen, O. J., “Exponential Stabilizaiton of Mobile Robots with Nonholonomic Constraints,” IEEE Transactions on Automatic Control, Vol. 37, No. 11, pp. 1791–1797, 1992.
Chen, J., Dixon, W. E., Dawson, M. and McIntyre, M., “Homography-Based Visual Servo Tracking Control Of A Wheeled Mobile Robot,” IEEE Transactions on Robotics, Vol. 22, No. 2, pp. 407–416, 2006.
Chwa, D., “Sliding-mode tracking control of nonholonomic wheeled mobile robots in polar coordinates,” IEEE Transactions on Control Systems Technology, Vol. 12, No. 4, pp. 637–644, 2004.
Lee, T. C., Song, K. T., Lee, C. H. and Teng, C. C., “Tracking Control of Unicycle-Modeled Mobile Robots Using a Saturation Feedback Controller,” IEEE Transactions on Control Systems Technology, Vol. 9, No. 2, pp. 305–318, 2001.
Park, K., Chung, H. and Lee, J. G., “Point Stabilization of Mobile Robots via State-Space Exact Feedback Linearization,” Robotics and Computer-Integrated Manufacturing, Vol. 16, No. 5, pp. 353–363, 2000.
Coelho, P. and Nunes, U., “Path-Following Control of Mobile Robots in Presence of Uncertainties,” IEEE Transactions on Robotics, Vol. 21, No. 2, pp. 252–261, 2005.
Tan, S. L. and Gu, J., “Investigation of Trajectory Tracking Control Algorithms For Autonomous Mobile Platforms: Theory and Simulation,” Proceedings of the IEEE International Conference on Mechatronics and Automation, pp. 934–939, 2005.
Zhang, Y., Chung, J. H. and Velinsky, S. A., “Variable Structure Control of A Differentially Steered Wheeled Mobile Robot,” Journal of Intelligent and Robotic Systems, Vol. 36, No. 3, pp. 301–314, 2003.
Shim, H.-S., Kim, J.-H. and Koh, K., “Variable Structure Control of Nonholonomic Wheeled Mobile Robot,” IEEE International Conference on Robotics and Automation, Vol. 2, pp. 1694–1699, 1995.
Barzamini, R., Yazdizadeh, A. R. and Rahmani, A. H., “A New Adaptive Tracking Control for Wheeled Mobile Robot,” IEEE Conference on Robotics, Automation and Mechatronics, pp. 1–6, 2006.
Park, J. H., Chong, K. T., Kazantzis, N. and Parlos, A. G., “Time-Discretization of Nonlinear Systems with Delayed Multi-Input Using Taylor Series,” KSME International Journal, Vol. 18, No. 7, pp. 1107–1120, 2004.
Park, J. H., Chong, K. T., Kazantzis, N. and Parlos, A. G., “Time-Discretization of Non-affine Nonlinear System with Delayed Input Using Taylor-Series,” KSME International Journal, Vol. 18, No. 8, pp. 1297–1305, 2004.
Zhang, Y. and Chong, K. T., “Discretization of Nonlinear Systems with Delayed Multi-Input via Taylor Series and Scaling and Squaring Technique,” Journal of Mechanical Science and Technology, Vol. 19, No. 11, pp. 1975–1987, 2005.
Lee, J. W., “A Systematic Gain Tuning of PID Controller Based on the Concept of Time Delay Control,” Int. J. Precis. Eng. Manuf., Vol. 9, No. 4, pp. 39–44, 2008.
Yang, T. T., Liu, Z.-Y., Chen, H. and Pei, R., “The Research on Robust Tracking Control of Constrainted Wheeled Mobile Robots,” Proceedings of International Conference on Machine Learning and Cybernetics, Vol. 3, pp. 1356–1361, 2005.
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Zhang, Y., Park, J.H. & Chong, K.T. Model algorithm control for path tracking of wheeled mobile robots. Int. J. Precis. Eng. Manuf. 11, 705–714 (2010). https://doi.org/10.1007/s12541-010-0083-3
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DOI: https://doi.org/10.1007/s12541-010-0083-3